An edge-case of this is using a pre-trained BERT model and then fine-tuning it for the new task and/or possibly adding extra layers to match the input and output shapes. Even for BERT, however, it was shown several times [1]}, [2]}, [3]}, [4]} that training on multiple tasks improves the performance [5]}. This would not be possible without a common model shared among the tasks.
Further related work is discussed in the respective sections when presenting individual NLP models and how they fit into this schema.
